The present disclosure relates to methods of dispensing a matrix material with homogeneous distribution of anisotropic filler particles through implosion, and structures generated by the same.
Anisotropic filler particles can serve a useful function when embedded within a matrix of another material. For example, conductive anisotropic filler particles embedded within a matrix of an insulating material can provide conductive paths through the insulating material through percolation of the distributed conductive anisotropic filler. Thermally conductive paths or electrically conductive paths can be provided through the matrix of the insulating material. Further, the anisotropic filler particles can add to the mechanical strength of the matrix.
The volume fraction of the anisotropic filler particles needed to provide percolation paths throughout the entirety of the matrix depends on the orientational anisotropy that the anisotropic filler particles provide. The orientational anisotropy depends largely on the ratio of the longest dimension of an anisotropic filler particle to the shortest dimension of the anisotropic filler particle, as well as the precise shape of the anisotropic filler particle.
In general, the greater the orientational anisotropy of the anisotropic filler particle, the less volume fraction is required to provide percolation paths within the matrix. In an illustrative example, in case anisotropic filler particles are shaped like cylindrical rods and have an aspect ratio (defined by the ratio of the length of a cylindrical rod to the diameter of the cylindrical rod) of about 500, a volume fraction of about 0.001 (i.e., 0.1% of the entire volume of the matrix) is sufficient to provide a connected network of percolation paths within the matrix. If the aspect ratio is about 200, anisotropic filler particles having a volume fraction of about 0.002 can provide a connected network of percolation paths within the matrix. If the aspect ratio is about 100, anisotropic filler particles having a volume fraction of about 0.005 can a connected network of percolation paths within the matrix. The number for a required volume fraction for providing a connected network of percolation paths can change as the shapes of the anisotropic filler particles changes (for example, into a disk).
While initial dispersions of anisotropic particles in a matrix are possible via many means of agitation, common dispensing techniques for dispersing such a dispersion into confined geometries leads to flow induced aggregation. A mechanism for such aggregation is illustrated in FIG. 1. Specifically, FIG. 1 illustrates a volume extending along the x and y direction (the y direction is perpendicular to the plane of the page) without boundaries and confined in the z direction between the z coordinates of z0 and z1. Injection of fluid typically results in a laminar flow with a non-uniform velocity field (illustrated with straight arrows) because the velocity of the fluid is zero at the horizontal planes of z=z0 and z=z1. Such non-uniform velocity field generates flow-induced rotation of particles embedded within the fluid. The greater the orientational anisotropy of the anisotropic filler particles within the fluid, the greater the rotation of the anisotropic filler particles. The rotation of the anisotropic filler particles induces physical contacts among the anisotropic filler particles, and results in agglomeration of the anisotropic filler particles.
Because the rate of agglomeration of the anisotropic filler particles increases with the amount of agglomerated anisotropic filler particles, the density of agglomerated anisotropic filler particles increases with distance from the injection point, which is represented by the vertical plane x=0. Agglomerated anisotropic filler particles can easily make physical contact with the boundaries (which are present at the horizontal planes of z=z0 and z=z1) and effectively precipitate out of the fluid once stuck at one of the boundaries. This phenomenon results in a non-uniform density of the agglomeration as a function of the distance (the value of x) from the injection point. Further, a non-uniform density of the anisotropic filler particles as a function of the distance from the injection point is present within the volume in which the injected fluid is present as illustrated in FIG. 2.
Injection of a matrix material including anisotropic filler particles into a volume between two bonded substrates faces the problem of agglomeration of the filler particles. For this reason, attempts to inject anisotropic filler particles at a density sufficiently high to provide a network of percolation paths resulted in non-homogeneous distribution of anisotropic filler particles in the past.